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A number of styles are specifically designed for a women’s physique, with unique fit and comfort characteristics built in. Be aware that a men’s version of a harness will not fit the same as a women’s version. Women–specific aspects include:

Women generally tend to have smaller, higher waists than their male counterparts, but larger hips and thighs, plus women’s hips usually sit at a different angle to men’s. Female-specific harnesses take all these things into account, and sometimes they look a bit more girly, too.

Consequently, women’s harnesses tend to have a bigger distance between the waist belt and the leg loops than men’s harnesses, which allows them to sit comfortably around the waist, rather than the hips. A harness that fits properly around the waist means you’re less likely to be flipped upside down if you fall; women have a lower centre of gravity than men so generally, if your waist belt is higher the more balanced you’ll be when you’re hanging from the rock – just don’t go too high or you’ll be flipping head-first instead!

For many women, men's harnesses work just fine. However, women's climbing harnesses address a few anatomical differences between the sexes. Women with smaller waists and bigger thighs may need a harness designed with these proportions in mind. Also, women with longer rises (the measurements between the crotch and waist) might do well with a women-specific harness because the leg loops are designed to be farther away from the waistbelt.

The other thing not mentioned in any of the above is that in some situations like long snow routes where you can't unrope, an alpine harness makes it easier for females to pee because they can undue the leg straps and leave the waist buckle completed.

On the other hand, they do make unisex climbing harnesses which are basically just buckles and straps as those will fit climbers of either gender.

From a male friend I heard that a wrongly designed or wrongly adjusted harness did hurt his private parts when it came under stress the first time.
In this case not permanent because he was wise enough to test the harness while still on the ground, but as he is likely to abseil it could have happened when he was committed on the way down.

He also told us about working in a harness for a whole shift, somewhere in the middle of an abseil inside a narrow part of a building, no way to get out for the breaks. In that case you will want the best fit and extra attention on comfort.

So not all males can use all harnesses, they have to be adjusted right for the person and the job the harness has to do.